Product Constancy Conditions

Product Constancy Conditions

i) When one factor of a product is increased by p% then the other factor will be decreased by (p/100+p X 100)%

 It means when one factor of a product is increased by n/d then the other factor is decreased by n/(d+n)

ii) When one factor of a product is decreased by p% then the other factor will be increased by
(p/100-p x 100)%

 It means when one factor of a product is decreased by n/d then the other factor will must be increased by n/(d-n)

Example 1:

If the price of a commodity be raised by 20% then by how much per cent a house holder reduce his consumption of the same commodity so that his expenditure does not increase.

Solution:

since here product (i.e., expenditure) is constant rate x consumption = expenditure

initially ------> 1 x 1 = 1

after change   1.2 * X = 1

X = 0.833 . therefore decrease in value = 16.66%


Example 2:

If the price of petrol falls down by 20% by how much per cent must a person increase its consumption, so as not to decrease the expenditure on this items?

Solution:

since product is constant
decrease by                              increase by

20% = 1/5 ------------------>       1/4 = 25%                ( n/d -----> n/(d-n))


Example 3:

Due to 50% increase in the price of rice. We purchased 5 kg less rice with the same amount of rs.60. What is the new price of rice?

Solution:

Increase in price                           Decrease in amount
50% = 1/2           ---------------->       1/3 = 33.33%

since the new quantity of rice decreased by 33.33% which is equal to 5kg it means initially there was 15kg rice to be used.

so, the initial price = rs.4           (60/15 = 4)

and final price = rs.6                   (60/10=6)


Example 4:

The length of a plot is decreased by 33.33%. By how much % the breadth of the plot will be increased so that the area remains constant?

Solution:

(Decrease)                             (Increase)

33.33=1/3 --------------->    1/2 = 50%